Plug-in Hybrid Electric Vehicles (PHEV) are an extension of existing hybrid electric vehicle (HEV) technology, in which a gasoline engine is supplemented by an electric battery pack and electric machines to gain increased mileage and reduced vehicle emissions. A PHEV utilizes a larger capacity battery pack than a standard HEV and it adds capability of recharging the battery from a standard electrical outlet. Because the battery pack has a larger capacity, the PHEV can be operated primarily by electric propulsion for a substantial distance, for example, a primary electric vehicle operation range (PER) of 10-40 miles, after a full battery recharges. The engine is only started to assist vehicle propulsion in limited circumstances such as high speed and/or high power demand operations due to system constraints. Such electrical-only or electrical-primarily operation is called EV or PEV operating mode, respectively. After the usable battery electricity is depleted, the engine takes over the primary role in vehicle propulsion by consuming fuel energy. By relying on electrical energy from the grid to charge the battery and then using that energy for a significant fraction of vehicle travel, the amount of fuel consumed by the PHEV is greatly reduced, especially when the traveling distance is close to the primary EV range.
Conventional HEVs buffer fuel energy and recover kinematic energy in electric form to improve the overall vehicle system operating efficiency. The fuel is the only energy source in general. For PHEVs, there is one additional source of energy; i.e. the amount of electric energy from the grid deposited in the battery after each battery charge event.
While conventional HEVs are operated to maintain the battery state of charge (SOC) at a nearly constant level, a PHEV uses as much pre-saved battery electric (grid) energy as possible before the next battery charge event; i.e. the relatively lower cost grid-supplied electric energy is expected to be used in priority and primarily for propulsion and for other vehicle functions after each charge. After the battery SOC decreases to a desired sustaining level or a lowest conservative level, the PHEV resumes operation as a conventional HEV. If no information is provided as to the expected driving distance until charge (DUC), in order to ensure that the grid-supplied electric energy is expended, the base PHEV control strategy always largely uses up the electric energy first and the engine takes over the leading role in vehicle propulsion when the battery is substantially discharged.
In FIG. 1, the two basic operation states of a PHEV: charge depleting (CD) and charge sustaining (CS) are illustrated. In the example shown in FIG. 1, a mostly charged PHEV (shown at a level 2 which is less than fully charged) is driven in the CD state for the first part of the trip, where the battery's state of charge (SOC) exhibits a net decrease between points 2 and 4. Due to the lower cost of electricity compared to fuel, the available battery electric energy is used for vehicle usage function before the next PHEV plug-in recharge event to largely displace fuel consumption. Since knowledge of the occurrence of the next battery recharge event is usually unknown, by default, the PHEV operation starts with CD process to assure battery depletion before the end of the trip.
During the CD operating state, according to the base PHEV energy management strategy, the battery's electric energy is used primarily to propel the vehicle, thereby maximally or near maximally depleting the electric energy stored in the battery. By primarily utilizing the battery energy to propel the vehicle early in the trip, the PHEV fuel consumption is minimized when the trip distance is close to the PER in EV/PEV (electric vehicle operation or in blended operation in which the internal combustion engine is used as little as possible) operations. Fully-charged PHEVs have an e.g. 10-40 mile PER in certain driving cycles, with the PER depending on the design goals, and thus the size of the battery pack, of the PHEV, as well as the driving cycles. At point 6, the trip has ended, the battery is recharged and attains the fully charged condition at point 7.
For example, let the total driver demanded PHEV drive power be Pdemand, the engine output power be Peng, the battery power be Pbatt and the electric power loss be Peloss, the following power balance equation holds for a PHEV:Pdemand=Peng+Pbatt−Peloss 
For simplicity, ignoring the battery internal energy loss and voltage variation, the change rate of state of charge is:dSOC/dt=ΔSOC/Δt=Pbatt/(Qbatt*Vbatt)where Qbatt is battery capacity in Ampere-hours and Vbatt is the battery voltage is Volts.
When the engine is operating, the fuel consumption rate can be approximated by:dFu/dt=Δfuel/Δt=K*Peng/ηeng where K is a simplified version of the fuel energy conversion ratio and ηeng is the engine power efficiency.
While the PHEV is operating in the CD state, it is consuming the useful battery SOC (the amount of battery SOC above a determined sustaining level) as much as possible to minimize fuel consumption before the next plug-in charge event. The PHEV is operated in EV mode when engine-on operation is not necessary, such that:Pdemand=Pbatt−Peloss and no fuel consumption occurs.
When engine-on operation is needed due to system constraints, such as vehicle speed limit or drive power limit, etc. or due to drive power assistance requirements in CD state, the engine power is limited to a low level in order to use Pbatt for primarily electric energy consumption:Pbatt=Pdemand+Peloss−Peng 
Since Peloss is usually small, it is ignored in the following descriptions for simplification.
In this case, the engine power is commanded at a minimum level between the drive power demand, Pdemand, and a pre-determined constant base power level, Peng—base≧0, if the battery power limit is not violated. Assume the engine is operated along a system optimal curve, and the base engine power level, Peng—base, is fixed at a constant small value with acceptable engine operating power efficiency to minimize fuel consumption in a trip with distance close to PER under a certain driving cycle. In the following description, the PHEV operation in CD state with maximal/near-maximal battery depletion strategy will be called Maximal Charge Depletion (MCD) state.
Once the battery's SOC decreases to a predetermined sustaining level (shown as point 4), the vehicle switches to the CS state, where the battery's SOC is kept within a certain range close to the desired sustaining SOC level. In CS mode, the vehicle is mainly powered by the engine (fuel energy), as is in a conventional HEV.
In summary, without knowledge of the occurrence of the next battery plugin recharge event, the PHEV operation is in favor of EV/PEV operation to use available battery electric energy for vehicle propulsion to displace fuel consumption during MCD operation. The PHEV is propelled at maximal/near-maximal battery power until point 4 is reached. The engine is kept in an off state or is kept at a low power level when on. After the usable battery SOC is depleted at point 4, the PHEV operation will in favor of HEV operation and it will be propelled primarily by the engine while the battery SOC is maintained around a constant sustaining level (CS from points 4 to 6).